Payday in a government town
My local supermarket is pretty small (as befits the smallish town I live in). There are eight tellers and an express lane for those who are only buying a few items. Most days there are only four out of eight tills working and the waiting time is negligible. But this is a government town, so almost everyone gets paid on the same day. Friday was payday, and like many teachers the journey from one payday and the next is a long, deep divide (“If you gaze into the abyss, the abyss gazes back into you”).
So as soon as my pay went in to the bank and my balance looked more healthy, I dived in to the supermarket to get some essentials and a few minor luxuries (toilet paper and chocolate with popping candy!). I was not the only one. By a long margin. The queue for the eight tellers was snaking this way and that way and all the way back to the Coca-Cola fridges. When I got close to the front of the queue I noticed that one of the supervisors was standing there calling out till numbers. I jumped to the conclusion that the automatic calling system wasn’t working, but when I commented on that (“Today of all days!”) she explained that it made things quicker if she called the next customer to the next free till.
No need to hurry
So why was it quicker? The supervisor could see when the teller was done with a customer and shoo the next mark in immediately, and this was quicker than waiting for the teller to push the button to get the automated system to call the next customer. You see, it doesn’t matter if the queue goes 200 metres back to the yoghurt fridges, a teller has no reason to rush. These ladies are going to be sitting there for their entire shift, pushing boxes of eggs, and tins of Milo and packets of Oreos past the scanner all the time. There is no incentive to work faster – another seven people are sharing the load, I am going to be here for hours anyway, so why rush?
In normal times this doesn’t matter – there is not really a need for tellers to work as fast as they possibly can. Customers only have to wait a few seconds or a minute at most before they get to the front of the queue, and (remember this is a small town) we are mostly pretty chill here. But on payday this attitude doesn’t work – the man in the queue behind me (right next to the Lemon Twists) was muttering about lalapanza (suggesting we would end up sleeping there overnight – or maybe that the tellers were sleeping?).
So the system that works 29 days out of 31 breaks down on a few days a month. How would it be possible to make it work better without breaking all the systems in place, or getting to some acrimonious place in the management-labour relationship?
The till operator cannot control…
The teller cannot control the person who arrives at their station. It could be a stressed-to-heavens mother who has only 10 minutes before she has to pick up her kids from ballet classes, who unpacks her trolley in record time. Or it could be Gramps and Granny whose only plan for the day was to choose which biscuits and tea they want for the next week, and who want to make this shopping expedition into a day-long foray. The teller has no control over how fast they unpack their trolley, how many items they are buying, their method of payment, and so on. What she can control is how quickly she calls the next customer – the time between completion of payment and her hitting that button.
When the queue hardly exists, there is no hurry. But suddenly on payday there are fifty people waiting with full trolleys where before there were only two or three. Now THIS is the time that we want the tellers to change from “pfft, no hurry, teller #3 will pick up the next one” to “waaah, gotta get them all!” mode. But with the current system, there is no motivation, no incentive for the tellers to do so.
Enter The Flag
Enter The Flag (or something similar). When the queue trails back as far as some landmark – for instance, it is so long that there are people standing at the “Animal Talk” magazine – then the flag gets raised. All the tellers know that when the flag goes up, the competition is ON! The teller with the quickest time between accepting payment and pressing the button for the next customer get a bonus (or a voucher, or whatever the company would like to offer). The teller whose average response time between the time payment went through and button was pressed also gets some reward. Oh, and the customers see that The Flag is up, they know that there is a priority rush on to get them on their way to that payday dinner.
I am confident that the sophisticated software run by supermarkets these days can track this data and do the simple processing required to award the Flag prizes. After all, they use my customer loyalty card to track what brands I buy and to keep an eye on my eating habits!
The Law of Unintended Consequences ensures that something will go wrong with the basic plan, so no doubt some tuning will be needed. For instance, on a busy day the Flag may go up and down four times – do we have four winners, or one overall winner?
By the time I had thought this through on Friday, I found myself at the front of the queue and the long wait was over!
So where is the math?
No mathematics in this post, just some thoughts about something that was annoying me at the time. The mathematics is actually there albeit it pretty simple – it’s just a matter of calculating a mean and determining the minimum of a couple of sets. It can be modelled by a simple Excel spreadsheet.
The actual mathematics of queueing is interesting and I wrote and introduction to queueing theory in this follow up post!